Numerical investigations of electromagnetic processes in a solid cylindrical shield

A mathematical model is suggested to describe the processes in a solid cylindrical shield in protection against an alternating magnetic field. The model is constructed with respect to the complex amplitude of magnetic vector potential. Since magnetic field lines are in a plane perpendicular to the axis of a cylindrical shield, the problem becomes two-dimensional. The electromagnetic parameters of the considered media are constant and isotropic. The plates at which the magnetic potential is set are the source of the magnetic field. A distribution of real and imaginary components of the complex amplitude of magnetic potential is described by four differential equations in the conducting medium and by two equations in the dielectric one. An equality of magnetic potential at both sides of the interface is predetermined at the interfaces. The Robin boundary condition provides equality of the magnetic vector potential to zero at an infinite distance from the shield. The obtained differential equation system supplemented with the boundary conditions can be numerically solved by the finite elements method using the Galerkin method. As a result, distributions of magnetic potential and magnetic field intensity in the absence and presence of a shield are determined; shielding attenuation is then calculated. It is found that, with increasing shield thickness and noise frequency, the efficiency of electromagnetic shielding is increased. The adequacy of the suggested model and technique of determination of the shielding efficiency is corroborated by comparison with the results of an analytical model for a copper cylindrical shield.     

有限宽金属平板对工频磁场的屏蔽

为了定量评估金属平板对工频磁场的屏蔽效果,在阐述了理想导磁材料和理想导电材料的磁场屏蔽原理基础上,基于无限宽金属平板屏蔽区域磁场解析式,通过计算域映射,推导了有限宽金属平板屏蔽区域磁场解析式.通过仿真分析了对称三相传输线屏蔽系统,讨论了导线组排列位置、屏蔽材料类型对屏蔽效果的影响.结果表明,采用解析式,可对有限宽金属平板的屏蔽效果进行快速计算,其准确性和计算效率优于现有电磁场分析软件所采用的数值求解方法,可对实际屏蔽系统的设计提供参考.     

EAST快控电源中空心电抗器的电磁屏蔽计算

针对EAST快控电源系统中空心电抗器运行时产生的磁场对周围电子设备干扰的问题,提出利用金属网屏蔽磁场的理论,通过解析计算得到单层和双层金属网屏蔽时屏蔽系数的表达式。参照现场实物建立多个三维模型,选择不同材料(DT4A,GO,1008steel)的金属网,采用三维有限元和Matlab仿真的方法,获得电抗器周围柜体屏蔽前后磁通密度的分布情况,进而分析了屏蔽系数与网孔数目、激励频率、距离的关系。结果表明,单层金属网屏蔽时,DT4A的屏蔽效果最好;双层金属网屏蔽时,DT4A/GO的屏蔽效果最好。总体而言,双层比单层屏蔽更加有效。对进一步研究空心电抗器的安全运行具有重要意义。     

Magnetic instability of ac multifilamentary superconductors in spatially distributed magnetic field

Alternating current (ac) superconducting machines such as superconducting generators, transformers, or resistive current limiters need large‐current‐capacity conductors. These conductors are generally fabricated as multistrand cables stacked with multifilamentary NbTi superconductors whose current capacity is a few tens of amperes. ac quench current degradation has often been observed in ac use of such multistrand cables. Several reasons for this degradation have been pointed out: nonuniformity of each strand current, mechanical disturbances, thermomagnetic instability, and ac losses. However, it has not as yet been overcome. Since the angle between the strand axis and the cable axis changes along the cable axis in multistrand cables, the strands are exposed to a spatially (axially) distributed magnetic field, which has longitudinal and transverse components changing periodically due to multiple cabling. This paper mainly discusses the thermomagnetic instability due to the distributed transverse magnetic field, which was compared with the self‐field instability and the longitudinal field instability experimentally and theoretically. It was confirmed that the ac quench current degradation due to the distributed transverse field could be induced by the following: nonlinear E–j characteristic, strong dependence of E–j characteristic on magnetic field in low field region, uniformity of the axial current profile inside the superconductor with the high resistive matrix, and the poor thermal diffusion of CuNi/NbTi composites. © 2000 Scripta Technica, Electr Eng Jpn, 131(1): 45–55, 2000     

Design of actively shielded main magnets: an improved functional method

An improved functional approach for designing MRI (magnetic resonance imaging) main magnets with active shielding is presented. By nulling one or two external moments as well as a certain series of internal moments of the magnetic field, new designs with improved shielding in combination with or without shorter magnet lengths are obtained. The improved method can be employed to design short and practical superconducting magnets at any given field strength. The resulting designs yield the desired field homogeneity inside the region of interest without using superconducting shim coils. This approach requires only a modest amount of computing power. One of the design steps, a contour plot of the continuous current solutions, can be utilized to study stretch goals for favorable design parameters.     

Influence of a longitudinal magnetic field on the vibration frequencies of ferromagnetic plates

The vibration of rectangular ferromagnetic plates in a longitudinal magnetic field is considered. Formulas are derived for the eigenfrequencies and form of vibration of conductive and dielectric rectangular ferromagnetic plates. The influence of a longitudinal magnetic field on the vibration frequency of plates with different attachment of the edges is investigated.     

Distribution of magnetic induction along hollow core of round section in constant homogeneous magnetic field

The results and an analysis of experimental studies of the distribution of the average relative magnetic induction in the cross section along the longitudinal axis of a hollow cylindrical ferromagnetic core of a round section magnetized by a homogeneous constant magnetic field are presented. A new formula is presented for calculations that take into consideration the thickness of the wall of the core and the dependence of the magnetic characteristics of its material on the size of the magnetizing field. A comparison has been made of the results of calculations and experiments for hollow cores of different geometries and the various magnetic characteristics of a material in a wide range of changes in the magnetizing field. The scope of the formula is shown.     

Construction of combined models of the properties of bulk high-temperature superconducting materials

The article contains the results of research that was aimed at improving the models of properties of bulk high-temperature superconducting (HTS) materials, which are necessary for numerical analysis of electromagnetic fields in electrical devices containing elements of high-temperature superconductors. Approximating combined models for a set of transport and bound currents are considered, which are determined, respectively, by the resistive model for currents and the nonlinear hysteresis model for the magnetization. The model of transport currents is based on the known types of the critical-state model. The material-magnetization model is composed for a set of magnetic moments of elementary superconducting cylinders with diameters that are much smaller than their length, which are oriented in the direction of the principal anisotropy axis of the material. The approximation to the actual conditions is realized by the statistical characteristics that specify the possible changes in the critical current density, the critical field strength, and the spatial orientation of the basic axes of the elementary cylinders. The results of studies of a laboratory model, which consists of a cylindrical HTS element and an annular permanent magnet, are presented and compared with the results of electromagnetic-field calculations according to the proposed models of properties.     

EMP作用下的电缆耦合及屏蔽效能试验分析

介绍了三同轴法、线注入法、功率吸收钳法、混波室法等电缆屏蔽效能测试方法.进行了电磁脉冲作用下的同轴电缆和裸线耦合试验,探讨了该环境下同轴电缆屏蔽效能的测试方法.试验分析表明,电缆耦合后的波形为衰减振荡波,振荡周期正比于电缆的电长度,频谱与照射场的频谱不一致,裸线的耦合输出衰减较快.根据试验数据,采用峰值场强法计算的电缆屏蔽效能与峰值电压法的结果吻合,所以可采用峰值场强法对电缆进行电磁脉冲的屏蔽效能测试.电磁脉冲作用下的同轴电缆屏蔽效能较相当频段连续波作用下的略低.     

Increase of inductance ratio of flat type fault current limiter with high‐Tc superconducting disk

Fault current limiters (FCLs) are expected to reduce fault current and improve stability of power systems. A flat type fault current limiter consisting of the pancake primary winding and a high‐T_c superconducting (HTS) disk was proposed as a modified version of a conventional magnetic shield type of the FCL with the superconducting cylinder. The flat type FCL has the advantage of being manufactured smaller than the cylinder type FCL. It is pointed out, from a magnetic field analysis, that the volume of the flat type FCL is smaller than that of the cylinder type FCL with same magnitude of the limiting inductance. Further, the magnetic field analysis suggests that a high inductance ratio can be realized by radially enlarging both the primary winding and the HTS disk, stacking the FCL modules in layers and sandwiching the primary winding with superconducting disks. © 2006 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Calculation of magnetic shielding of a substation at powerfrequency using FEM

The finite element method (FEM) is used for analyzing the shielding effectiveness of an eddy current shield applied to a 10/0.4 kV substation. The influence of the shield extension is studied, and a calculated magnetic field attenuation of 30 dB is obtained for a 5 mm aluminum shield applied on the ceiling and the walls. With a 3D model, the eddy current distribution in the shield is studied, giving guidance for door positioning. Here, the insertion of a door in the shielded wall off the paths of the main eddy currents is found to create only a locally elevated magnetic field. With a simplified 2D model, the influence of shield conductivity is also analyzed. An increase of the conductivity over that of aluminum here gives a limited shielding improvement     

高压自耦变压器肺叶磁屏蔽特性的数值计算与分析

针对一种新型的器身磁屏蔽——肺叶磁屏蔽自身以及其在变压器中的设计问题,以一台容量为334MV?A、带有肺叶磁屏蔽的单相自耦变压器为研究对象,首先应用三维频域非线性有限元法分析了肺叶磁屏蔽对变压器结构件、绕组区域漏磁场以及杂散损耗的影响;然后,以漏磁场分析以及杂散损耗计算为手段,以变压器油箱、夹件、拉板、油箱屏蔽以及肺叶磁屏蔽的磁感应强度(或损耗密度)作为观测目标,研究肺叶磁屏蔽安装位置以及尺寸对变压器漏磁场的影响,并通过负载损耗试验将有限元计算所得结果与实验值进行对比,验证分析的有效性;最后,针对肺叶磁屏蔽自身可能出现的局部过热问题,设计三种不同的肺叶磁屏蔽油路结构,基于有限体积法对比分析不同油路结构下肺叶磁屏蔽的油流、温升特性。对肺叶磁屏蔽特性的系统分析可为其设计以及其在变压器中的设计提供指导,具有重要工程意义。     

A numerical study of the efficiency of a cylindrical electromagnetic shield

Electromagnetic shields are widely used for protecting electrical equipment and cable lines from the influence of natural and artificial electric and magnetic fields. A 3D mathematical model of a solid cylindrical shield for protection from the effect of an alternating electromagnetic field produced inside a cable has been proposed. The model has been constructed using the finite-element method in the ANSYS HFSS software. Two electromagnetic-field sources have been considered: noise in the inner conductor (cable core) and a coaxial circuit, in which the shield is an outer working conductor. The electromagnetic-field distribution over the cable is described by the Maxwell equations, which are transformed into the Helmholtz vector equation with respect to the electric-field component so that the finite-element method may be used. The electromagnetic parameters of the considered media are constant and isotropic. The shielding properties have been studied for a copper cylindrical shield in the frequency range of 1–100 MHz. As a result of the mathematical solution, the distributions of electromagnetic-field intensities in the model have been obtained. To determine the shielding properties of a cable, the transfer impedance and shielding attenuation have been used. The adequacy of the model and technique for determining the efficiency of the screening has been verified by means of comparison between the obtained data and results of the analytical model.     

Magnetic and conductive shielding for air‐core pulsed alternators in railgun systems

Magnetic and conductive shielding are the alternative choices for air‐core pulsed alternators (air‐core CPAs) in electromagnetic railgun systems. Because of the absence of ferromagnetic materials in the air‐core alternators, the flux density inside can be 3–5 T. Electromagnetic shielding is needed to protect the surrounding electronic devices and humans from exposure to high oscillating magnetic fields. Electromagnetic shielding changes the distribution of the magnetic field and the corresponding winding inductance, as well as the output performance of the powering the railgun. This paper mainly concentrates on a GW‐scale, four‐phase air‐core CPA‐based railgun system. The magnetic and conductive shielding are adopted correspondingly. The effectiveness of shielding and electric performance are investigated in detail. Using the co‐simulation method, an instructive comparison is made between the magnetic shield and the conductive shield, which is meaningful to the design of the electromagnetic shielding of air‐core CPAs for railgun systems. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

用于磁探测的铁磁屏蔽体的形状与尺寸设计

针对高精度磁探测条件下铁磁屏蔽壳体的形状与尺寸设计问题,从屏蔽体的屏蔽效能与在空间产生的附加干扰场出发,对比分析了不同形状、尺寸屏蔽体的屏蔽效能与综合磁化系数,提出了屏蔽壳体形状、尺寸设计依据。按照该依据,在相同厚度、相近尺寸条件下,球壳整体性能最优,圆柱与椭球壳性能相近且次之,方壳性能最差;在相同厚度、相同形状、相近容积条件下,屏蔽体各尺寸比例为1时,壳体整体性能最优。     

Halbach磁体中柱面匀场线圈的设计方法

Halbach磁体场强高、体积小,是永磁台式核磁共振波谱仪的理想磁源。为开发高分辨永磁台式核磁共振波谱仪,需要使Halbach磁体的磁场达到高度均匀。引入在超导磁体中被广泛使用的鞍型线圈,设计了一种由鞍型线圈组成、能够对Halbach磁体的横向磁场进行补偿的柱面匀场线圈。仿真和实验结果证明了设计方法的正确性。     

电力变压器磁屏蔽模型涡流场和损耗的计算与测量

大型电力变压器铁磁结构件中产生的电磁损耗会导致局部过热并使相关的绝缘部件受到损害,进而危及整个变压器的正常运行,对面向工程的国际TEAM(Testing Electromagnetic Analysis Methods)Problem 21的磁屏蔽基准模型的涡流场和损耗进行了计算和试验测量研究,考虑了模型中铁磁材料的非线性、各向异性及磁滞等特性,提出了用于分离激励线圈电阻损耗和涡流损耗的测量方法(漏磁通补偿线圈测量装置),并用MagNet软件进行了数值计算.基准模型的计算和测量结果相吻合,验证了计算方法和软件的有效性.     

空心电抗器的复合被动屏蔽结构的电磁性能分析

针对空心电抗器的漏磁场问题,通过加装多层复合式磁屏蔽装置,对空心电抗器进行磁场屏蔽,以减少目标区域内的磁场强度,达到保护目标区域内操作人员健康和设备安全的目的。在一定频率范围的正弦电流激励下,利用坡印亭定律和麦克斯韦方程推算出空心电抗器屏蔽体涡流损耗和目标观测点的屏蔽效能解析计算公式,并在涡流场中求解不同结构磁屏蔽体各层的涡流损耗和目标区域内观测点的屏蔽效能,并利用有限元仿真,对不同结构磁屏蔽的电磁性能进行评估,从而为复合式被动磁场屏蔽设计提供相应的建议和参考。     

Stabilization for thermomagnetic instability of CuNi/NbTi superconducting wire in spatially distributed magnetic field

Thermomagnetic instability in superconducting wires composing multistrand cables is a problem in the development of cables with large current capacity. This paper elucidates the quenching properties of ac superconducting wires in a distributed magnetic field applied to the strands in the cable, and the stabilization of the ac superconducting wires considering the effect of the longitudinal magnetic field or the fraction of copper embedded in each strand. First, the degradation of the quench current of CuNi/NbTi superconducting wires in a distributed magnetic field is exhibited with simple test samples. Second, the quench properties of the strand in a (6 + 1)³ cable and the optimal twist pitch of the cable for high stabilization are discussed. Last, the effect of copper on the quench properties of the strand and the appropriate fraction of copper for suppression of quench current degradation in a distributed magnetic field are discussed. © 2001 Scripta Technica, Electr Eng Jpn, 135(4): 26–34, 2001     

电力变压器三维涡流场计算与屏蔽问题分析

针对大型电力变压器漏磁场及局部过热问题,笔者应用三维涡流场有限元分析方法对变压器夹件及油箱进行了漏磁场及涡流损耗计算,在此基础上分析了局部过热问题并给出了相应的屏蔽措施,对屏蔽效果的影响因素进行分析,为变压器屏蔽的合理设计提供了参考依据.